Arrangement of a 4Pi Microscope for Reducing the Confocal Detection
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Arrangement of a 4Pi microscope for reducing the confocal detection volume with two-photon excitation Nicolas Sandeau∗and Hugues Giovannini† Received 16 November 2005; received in revised form 7 February 2006; accepted 8 February 2006 Institut Fresnel, UMR 6133 CNRS, Universit´ePaul C´ezanne Aix-Marseille III, F-13397 Marseille cedex 20, France The main advantage of two-photon fluorescence confocal microscopy is the low absorption obtained with live tissues at the wavelengths of operation. However, the resolution of two-photon fluorescence confocal microscopes is lower than in the case of one-photon excitation. The 4Pi microscope type C working in two-photon regime, in which the excitation beams are coherently superimposed and, simultaneously, the emitted beams are also coherently added, has shown to be a good solution for increasing the resolution along the optical axis and for reducing the amplitude of the side lobes of the point spread function. However, the resolution in the transverse plane is poorer than in the case of one-photon excitation due to the larger wavelength in- volved in the two-photon fluorescence process. In this paper we show that a particular arrangement of the 4Pi microscope, referenced as 4Pi’ microscope, is a solution for obtaining a lateral resolution in the two-photon regime sim- ilar or even better to that obtained with 4Pi microscopes working in the arXiv:physics/0610036v1 [physics.bio-ph] 6 Oct 2006 one-photon excitation regime. Keywords: Resolution; Fluorescence microscopy; 4Pi microscopy; Confocal; Detection volume; Two-photon excitation ∗E-mail: [email protected] †E-mail: [email protected]; Tel: +33 491 28 80 66; Fax: +33 491 28 80 67 1 1 Introduction Strong efforts have been made in the last decade to improve the resolution of fluorescence microscopes. Indeed, localizing marked species with sub- wavelength accuracy gives precious information for cell biology applications. In particular, in fluorescence correlation spectroscopy experiments made with confocal microscopes, varying the detection volume is the key task for study- ing, at different scales, molecular mechanisms inside cells [1, 2, 3]. For re- ducing the lateral extent of the detection volume, high numerical aperture immersion objectives have been developed [4]. However, the axial extent of the point spread function (PSF) of conventional confocal microscopes remains about four times larger than its lateral extent. To solve this problem, various solutions, mostly based on the use of interference phenomena, have been pro- posed [5, 6, 7, 8, 9]. In particular the coherent superposition of the excitation wavefronts and that of the emission wavefronts passing through two oppos- ing lenses, has led to the development of the 4Pi microscope [10, 11]. It has been shown that, with 4Pi microscopes working with one-photon excitation, the axial resolution can be improved by a factor 3 to 7 over that of confocal microscopes and related systems [12]. However, with this technique, the fo- cal maximum is also accompanied by interference side lobes whose maximum intensity exceeds 50% of the maximum intensity in the focal point. In this case classical image deconvolution algorithms do not work properly and the resolution along the optical axis is not improved. To overcome this difficulty, various solutions have been proposed. Among them one can cite the 4Pi type C microscope with two-photon excitation [13, 14, 15] . In this set-up, two opposite microscope objectives are used to illuminate coherently the fluores- cent sample from both sides and, simultaneously, to add coherently the two emitted beams. The PSF is the result of the superposition of two systems of fringes: the one produced by the pump beams, the other produced by the emitted beams. The strong difference between the pump wavelength and the wavelength of luminescence in the two-photon excitation regime leads to different intensity spatial distributions of the fringes along the optical axis. The consequence is that a strong reduction of the amplitude of the side lobes of the PSF is obtained. This is a very interesting solution which strongly improves the resolution along the optical axis while preserving the main ad- vantage of two-photon excitation which is the low absorption of live tissues at the wavelength of operation [13, 16]. However, due to the larger wavelength of the pump beams used in the two-photon excitation regime, the transverse 2 resolution is worse than in the case of one-photon excitation [14, 15]. Other solutions based on the used of variable density filters for shaping the axial component of the PSF have also been proposed [17]. Recently it has been shown theoretically that a particular arrangement of 4Pi microscope, referenced as 4Pi’ microscope [18], made possible an in- crease of the lateral resolution in one-photon excitation regime. In the present paper we extend the domain of application of the 4Pi’ microscope. We de- scribe the vector model that can be used to compute the image of a dipole through the 4Pi’ microscope. Thanks to numerical simulations based on this model, we show that the 4Pi’ microscope working in the two-photon regime cumulates the advantages of the 4Pi microscope working with one-photon regime and those given by two-photon excitation. In particular numerical, calculations show that the excitation volume of the 4Pi’ type C microscope working with two-photon excitation is comparable to or even smaller than the excitation volume obtained with 4Pi type C microscopes working in the one-photon excitation regime. The main advantage of this solution is that it keeps a high resolution when the pinhole size increases, leading to high signal-to-noise ratio for practical applications. 2 Set-up In 4Pi microscopes the axial extent of the PSF is reduced, with respect to classical confocal microscopes, by taking advantage of the variation of the optical path difference (OPD) along the optical axis between the pump beams (case of 4Pi type A microscopes), between the emitted beams (case of 4Pi type B microscopes) or between both the pump beams and the emit- ted beams (case of 4Pi type C microscopes) [11].The displacement of the luminescent source in the transverse direction has no influence on the OPD between the emitted beams. Thus, for identical microscope objectives and similar exit pupil diameters, the resolution is improved only along the op- tical axis and the lateral extent of the PSF of 4Pi microscopes is identical to that of classical confocal microscopes working at the same excitation and emission wavelengths. Recently a configuration of the 4Pi microscope, called 4Pi’ microscope, has been proposed [18]. In this microscope an interference phenomenon is produced by the displacement of the luminescent source in the transverse direction. This interference phenomenon is used to reduce the lateral extent of the PSF. The set-up is represented in Fig. 1. It is based on 3 a 4Pi microscope in which an image inversion has been added in one arm. The pump laser is assumed to be transverse monomode TEM00 in order to ensure the spatial coherence of the two incident beams which interfere as in a classical 4Pi microscope. The beam is expanded in order to give a constant illumination within the aperture of the objectives. We assume that the OPD between the two incident beams is equal to 0 in the common focal focus F of the microscope objectives. We also assume that the chromatic dispersion in the two arms is perfectly compensated. In order to point out the differences between the 4Pi microscope and the 4Pi’ microscope we have represented, in Fig. 2, the equivalent optical schemes of the two arrangements. We have considered a single dipole source placed in the vicinity of the common focus F of the two microscope objectives. In the 4Pi microscope and in the 4Pi’ microscope the two beams emitted by dipole D pass through the objectives. In both microscopes the displacement of dipole D from focus F creates a S LASER Photodetector L Pinhole Image inversion Notch Filter system BS Fluorescence Fluorescence O1 O2 M M Figure 1: Set up of the 4Pi’ microscope. With respect to the classical 4Pi microscope, an image inversion system is added in one arm of the interfer- ometer. The optical path difference of the interferometer is assumed to be equal to 0 for the incident wavelength and for the emission wavelength. M are mirrors. BS is a beam splitter. 4 x x D ID D and ID y z F z y ID’ ID’ FP O Figure 2: Equivalent optical schemes, for emission, of the 4Pi microscope and of the 4Pi’ microscope. ID is the virtual source in the 4Pi microscope. ID’ is the virtual source in the 4Pi’ microscope. z is the optical axis of the system, O is the microscope objective. The two microscope objectives O1 and O2 of the set-up of Fig. 1 are assumed to be identical. (a) View in a plane containing the optical axis. (b) View in a plane orthogonal to the optical axis. F is the common focus of O. FP is the focal plane of O. second virtual source. However, the location of this virtual source depends on the arrangement (see Fig. 2). In the 4Pi microscope the two beams are emitted by dipole D and by the virtual source ID. In the 4Pi’ microscope the two beams are emitted by dipole D and by the virtual source ID’. D and ID are symmetric with respect to focal the plane FP of the microscope objectives, while D and ID’ are symmetric with respect to focus F. All the differences between the 4Pi microscope and the 4Pi’ microscope lie on these two different symmetries. 3 Vector model For comparing the CEF of the 4Pi microscope with that of the 4Pi’ micro- scope, for a source located around focus F, taking into account the vector nature of the dipolar emission, it is necessary to use a complete description of the image formation through the microscope objectives.